Bullet Rating vs Online rating

Yes, and another factor is attitudinal. I have a philosophical hate for bullet nad blitz; there is no "truth" about the positions at such speed. In the times of Capa and Maroczy bullet would be called "skittles".

I have also trained myself to move slowly in ANY position. I am not a patient person. So it was hard to do. But even if I have a mate in 1 or a queen and king against king I have trained myself to still take a minute at least to move. This and my personal psychology of sitting on my hands when I know that I am winning - as soon as I know this I will take about 5 minutes for the next move - is all excellent technique for long time controls but lousy [clearly] at blitz or bullet.

I find it abolutely possible that someone could be below 1000 at bullet and 2600 at long time controls.

For me, the irony is that I have more problems with time in 3 0 (and just in general!) than I do in bullet. I think it's because bullet basically forces me to be fast, whereas the slower time controls give me the opportunity to dig my own grave by taking huge amounts of time in the opening

Not only are the two different, but few take bullet games seriously. You generally play bullet chess to relax. If you took bullet games seriously you would not use the same strategic openings you use for chess but would play aggressive tactical openings and not worry about material but strive for the initiative at any cost. Most players will continue to use the openings they are familiar with.